A:I concede, four helmets does seem like a waste. Then again, any one helmet is going to compromise just about every usage, so theres an argument to be made that four helmets is the best route.
That said, its helpful to think of how the different activities you mention affect helmet usage. I think the best argument for a purpose-built helmet can be found in cycling, where its easy to generate a lot of heat in a hurry. So a cycling helmet works best for that sport, something such as the Bell Array ($100). An excellent, light, well-vented helmet.
Kayaking helmets are not unlike climbing helmets, but tend to have a foam liner that could make them hot when climbing. So maybe take a climbing helmet kayakingPetzls Elios ($70) would do double duty nicely, in my view. It might even work for cycling, if youre doing sort of casual rides. And its actually intended as a bit of a multi-sport helmet.
For winter, ski helmets are designed to be warm with liners and ear covers and to give you a handy place to park your goggles. Cycling helmets are definitely out. But you could don a thin stocking hat and wear the Elios, and youd be just fine. Otherwise, Giros G9 ($100) gives you good skull protection at a reasonable price.